Kernel-Based Face Hallucination via Dual Regularization Priors

Recently, patch-based face hallucination methods have shown the ability for achieving high-quality face images. The high-resolution (HR) patches can be reconstructed by a linear combination of training patches, while the combination coefficients are learned according to the corresponding low-resolution (LR) patches. In order to reflect the local features, face images are usually divided into very small patches, e.g.
$3 \times 3$
for LR case. Though we assume the linear relationship between training patches, it may fail to obtain suitable combination coefficients due to the low dimension of LR patches. In this letter, the kernel function is utilized for mapping the LR patches into a high-dimensional feature space. By taking into account the nonlinear structures, it is more effective to estimate the combination coefficients in the kernel feature space. Furthermore, a pixel-based model is also employed according to the characteristics of face images, which is useful to compensate the local textures. The final HR face images are obtained from a global optimization function by an iterative process. Experimental results show the advantage of the proposed approach in both reconstruction error and visual quality.